No problems with waxed chains here in Texas during hot dry summers.
Even if I don't wipe down a freshly waxed chain or let the excess drip off, the excess will flake off during the first ride. A few flakes may appear between cogs, but it won't do any harm. It doesn't attract nearly as much road grime as wet lubes.
And if I let the freshly waxed chain drip the excess back into the pot, and wipe down the still-warm chain, there's only a thin layer on the external bits.
Straight Gulf wax is very hard compared with scented candles, and won't melt or drip in typical summer heat. Sometimes I add leftover scented candle wax to the crock pot, which softens it a little. Scented candles already contain a compatible solvent and are much softer (I used the stuff between spoke crossings on one bike with black spokes to reduce creaking noises). But I need to be careful to use low or medium heat to prevent smoking.
The only drawback I've found to waxed chains is they won't hold up to heavy rain. But I try to avoid riding my road bikes in wet weather anyway. (Especially after seeing the condition of the fork steerer in my 1993 Trek 5900 last week. Yikes.)
I use Park CL-1 on one hybrid, my errand bike. It's pretty tenacious stuff and clings despite rain. Only needs to be done once or twice a year. But the chain does get as grimy as you'd expect from any wet lube.